Find a formula for the inverse of the function \( k(x) = \frac{3-\sqrt{x}}{\sqrt{x}+2} \)

5th Ed: #39

\( x = \frac{3-\sqrt{k^{-1}(x)}}{\sqrt{k^{-1}(x)}+2} \)

\( x\sqrt{k^{-1}(x)}+2x=3-\sqrt{k^{-1}(x)} \)

\( x\sqrt{k^{-1}(x)}+\sqrt{k^{-1}(x)}=3-2x \)

\( \sqrt{k^{-1}(x)}(x+1)=3-2x \)

\( \sqrt{k^{-1}(x)}=\frac{3-2x}{x+1} \)

\( k^{-1}(x)=\left ( \frac{3-2x}{x+1} \right ) ^2 \)